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# How to factor 2x^2+x-1 ?

## i tried to factor it and i got $\left(2 x + 1\right) \left(x - 1\right)$ but my friend said the correct answer is $\left(2 x - 1\right) \left(x + 1\right)$

May 10, 2018

2x^2+x-1=color(blue)((x+1)(2x-1)

#### Explanation:

Factor:

$2 {x}^{2} + x - 1$

The method to use is called "splitting the middle term."

Multiply the coefficient of the first term by the constant.

$2 \times \left(- 1\right) = - 2$

Find two number that when added equal $1$ and when multiplied equal $- 2$. The numbers that meet the criteria are $2$ and $- 1$.

Rewrite the expression, splitting the middle term $x$ into $2 x$ and $- x$.

$2 {x}^{2} + 2 x - x - 1$

Factor out the common terms in the first two terms and the second two terms.

$2 x \left(x + 1\right) - \left(x + 1\right)$ $\leftarrow$ $- \left(x + 1\right) = - 1 \left(x + 1\right)$

Factor out $\left(x + 1\right)$.

$\left(x + 1\right) \left(2 x - 1\right)$